N. Austin-Bingamon, M. Goodman, R. Dominguez, R. Mayorga-Luna, D.S. Kim, K.P. Lee, K. Watanabe, T. Taniguchi, X.E. Li, Y. Miyahara
Texas State University,
United States
Keywords: KPFM, Kelvin probe force microscopy, moiré, moire, hBN, hexagonal boron nitride, t-hBN, twisted hexagonal boron nitride, FEM, finite element method, finite element analysis, numerical, COMSOL, electrostatics
Summary:
Moiré superlattices have been attracting significant attention because they can host a rich variety of correlated electronic phases. The periodic electrostatic potential on the surface of a twisted hexagonal Boron Nitride (t-hBN) bilayer or a multilayer (moiré potential) can be used to impose a moiré potential on an adjacent functional layer and modulate its electronic band structure. This moiré potential originates from spatially alternating electric polarization at the interface of twisted hBN layers (Fig. 1a in extended abstract) and the depth and period of the potential can be tuned by the twist angle and the top hBN layer thickness [1]. We confirmed these theoretical predictions by measuring the moiré potential by Kelvin probe force microscopy (KPFM) (Fig. 1b-d in extended abstract) [2]. We also performed finite element modeling (FEM) of the KPFM measurements with COMSOL Multiphysics, including the effect of both the tip and the substrate. Leveraging an analytic formula for the electric dipole density at the t-hBN interface by Zhao et al. [3], our model predicts the electric potential and charge distribution of the t-hBN system. We first modelled the system in the absence of an AFM tip to predict the true surface potential. In addition, we modelled the actual Kelvin probe measurement process by including the AFM tip in the simulation. An electrical bias is applied between the AFM tip and the sample bottom layer. By finding the bias voltage which minimizes electrostatic force on the tip, we predict the potential which would be measured by KPFM. From our model, we found that the measured potential by KPFM is within 20% of the true value for all sample and AFM tip geometries tested. The dielectric thickness and permittivity, both below and above the t-hBN bilayer, were found to influence the KPFM measured potential at the sample surface. Implications for calculating the accurate surface potential from KPFM data are discussed. In addition, we find that increasing the dielectric constant on the bottom side of the t-hBN bilayer enhances the moiré potential on the top side. Implications for engineering the strength of potential modulation are discussed. Finally, we will present the comparison between the experimental and finite-element simulation results and discuss the physical basis of KPFM in the context of our sample. We gratefully acknowledge fundings from the National Science Foundation (DMR-2122041, DMR-2044920, DMR-2117438, DMR-1720595 and DMR-2308817). References [1] P. Zhao, C. Xiao and W. Yao “Universal superlattice potential for 2D materials from twisted interface inside h-BN substrate”, npj 2D Mater.Appl. 5, 38 (2021). [2] D.S. Kim, R.C. Dominguez, R. Mayorga-Luna et al. “Electrostatic moire potential from twisted hexagonal boron nitride layers”, Nat. Mater. 23, 65-70 (2024). [3] Zhao, P., Xiao, C. & Yao, W. Universal superlattice potential for 2D materials from twisted interface inside h-BN substrate. npj 2D Mater Appl 5, 1–7 (2021).